Slab theorem and halfspace theorem for constant mean curvature surfaces in H2 x R Hauswirth, Laurent Menezes, Ana Rodríguez Pérez, María Magdalena We prove that a properly embedded annular end of a surface in H 2 ×R with constant mean curvature 0 < H≤ 1 / 2 0<H≤1/2 can not be contained in any horizontal slab. Moreover, we show that a properly embedded surface with constant mean curvature 0 < H ≤ 1 / 2 0<H≤1/2 contained in H2 × [ 0 , + ∞ ) H 2 ×[0,+∞) and with finite topology is necessarily a graph over a simply connected domain of H 2 H 2 . For the case H = 1 / 2 H=1/2, the graph is entire. 2023-06-23T11:18:36Z 2023-06-23T11:18:36Z 2022-08-25 journal article Laurent Hauswirth, Ana Menezes, Magdalena Rodríguez, Slab theorem and halfspace theorem for constant mean curvature surfaces in H 2 ×R. Rev. Mat. Iberoam. 39 (2023), no. 1, pp. 307–320 DOI 10.4171/RMI/1372 https://hdl.handle.net/10481/82771 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional European Matematical Society